Question

Two thermodynamical processes are shown in the figure. The molar heat capacity for process \( A \) and \( B \) are \( C_A \) and \( C_B \). The molar heat capacity at constant pressure and constant volume are represented by \( C_P \) and \( C_V \), respectively. Choose the correct statement.

• A. \( C_B = \infty, \, C_A = 0 \)
• B. \( C_A = 0 \, \text{and} \, C_B = \infty \)
• C. \( C_P > C_V > C_A = C_B \)
• D. \( C_A > C_P > C_V \)

Answer 1

The Correct Option is B

To address this problem, we will examine the thermodynamical processes depicted in the figure and the given options, focusing on the relationships between molar heat capacities. The relevant molar heat capacities are \( C_A \), \( C_B \), \( C_P \), and \( C_V \).

The figure illustrates two primary processes, designated as \( A \) and \( B \). Let's analyze each individually:

1. Process A: This process is represented by a vertical line on the log-log plot of pressure (\( P \)) versus volume (\( V \)), indicating no change in volume (\( dV = 0 \)). This is an isochoric process, which involves the heat capacity at constant volume. Since \( C_A \) is associated with this process, and no work is done in an isochoric process where added heat solely increases internal energy, \( C_A = 0 \).
2. Process B: This process is depicted as a horizontal line, signifying a constant pressure (\( dP = 0 \)). For an isobaric process, the heat capacity is related to volume changes at constant pressure, quantified by the molar heat capacity \( C_P \). If \( C_P \) is involved, the slope implies that heat input leads to a state where the theoretical heat capacity is infinite, as all added heat might result in a phase change or no temperature alteration. Consequently, \( C_B = \infty \).

The option that aligns with our analysis is:

\( C_A = 0 \, \text{and} \, C_B = \infty \)

This conclusion is supported by the analysis of the thermodynamical processes and their graphical representation on the log-log diagram.